Tether visibility in daylight?

Robert H. McNaught, Anglo-Australian Observatory (RMN@aaocbn2.aao.gov.au)
Fri, 15 Mar 1996 10:59:33 +1100 (EST)

Could the tether become visible in daylight?

Treating the tether as a vertical cylinder, the geometry producing a specular
reflection is quite straight forward.  It can only occur in daylight.
Two conditions must be met;

a) the tether must be in the opposite azimuth to the Sun in the sky and

b) the angle of the observer below the "equator" of the tether must equal the
   angle of the Sun above its "equator".

Defining

Es = elevation of the Sun at time tether is opposite in azimuth

Et = elevation of tether at this time

 A = arc subtended at Earth's center between observer and tether
  (= great-circle arc on Earth's surface between observer and sub-tether point)

Gives the necessary relation
                                  Es = 2A + Et

for a specular reflection to occur.

These quantities are either easily calculated or available from the ephemeris.
The angle "A" can be easily found from
                                        sin(A) = (D . cos(Et)) / (Rphi + H)
where

D = distance of tether from observer
H = Height of tether above geoid
Rphi = radius of Earth at tether latitude

Rob McNaught